The shock wave and cumulative arrival and departure curve techniques are staples of traffic analysis, particularly for the modeling of freeway congestion, but the literature contains numerous suggestions that they are not compatible. Three numerical examples illustrate that although the two models define queue lengths in different ways, they are compatible, yield identical estimates of travel time and delay, and provide additional insight into the nature of freeway congestion when used together instead of individually.
Public bike-sharing systems in many countries provide convenience as users can rent or return a bike freely at any station, but this may cause a demand–supply imbalance of the bike inventory for certain stations. To solve this issue, this research develops a bike-relocation strategy including both demand prediction and relocating route optimization. First, the bike demand is estimated by a least-square boosting algorithm, and numbers of relocating bikes are decided comparing bike inventories at each station. Second, based on predicted demand, the number of transporting vehicles and relocating routes are optimized by genetic algorithm. The strategy aims to minimize service vehicle numbers and relocating time with selective pick-up and delivery. The proposed strategy is evaluated by applying it to a real-world public bike system in Gangnam-district in Seoul, South Korea, and the results show the system can be improved significantly. Specifically, the bike demand satisfaction ratio increases from 0.87 to 1.00 in the morning peak hour, which shows that the proposed strategy better satisfies the bike demand. The uniformity of spare inventory is also improved, as a coefficient of variation decreases from 0.73 to 0.56. The reasonableness index, which reflects a sufficient number of bike stands, indicates 87% and 92% stations have a proper number of stands at morning peak hour and 24 h, respectively, with respect to predicted demand. The results show that the bike system with the proposed strategy has more reliability with stable inventory, and the operating cost could decrease with fewer relocating vehicles and optimized vehicle routes.
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